So I would like to know, how would it be possible to concentrate sufficiently for culture (for the purpose of earlier cultural victory) without dangerously negleting the military ? Also I would be interested to know how early it is actually possible to "safely" achieve the cultural victory ?
If your main concern is not getting defeated militarily on your way to a culture victory, then probably be the best piece of advice I can offer is do not adopt a religion. If you have a state religion you are bound to get some big diplomatic penalties with someone out there, and that someone will more than likely attack you because you're going to be militarily weak. So skip the state religion if you're worried about getting attacked.
More generally speaking, pay close attention to diplomacy. Be as friendly as you can with the most powerful and advanced nations. Identify who their enemies are, and do not trade with them. But do give in to demands for tribute from anyone and everyone. Consider even giving in to demands to switch civics or religions, if it won't hurt you too much (e.g., you can switch back again quickly).
You've already recognized that you cannot neglect your military completely. You can usually get away with a weak military at the very beginning of the game because most AIs aren't very aggressive then. Just don't do anything to make them mad at you. But by the time you have 3 or 4 cities in place you should have at least one of them that is devoting a lot of its time to building military units. That won't be enough for you to keep up with the AI in military size, but you're not going on the offensive. All you need are enough troops to fight off a single AI if he decides to attack in the middle part of the game when you're on par with them technologically. This shouldn't be that hard, because the AIs are lousy at military tactics.
In the later stages of the game you can stop building military again because by that time the AIs armies will be so much bigger and better than yours that you can't possibly beat them.

Once you're fully committed to culture production your best hope is to just concentrate on getting your Legendary cities as fast as possible. Building more Macemen or Grenadiers will not help you if the AI has huge armies of Infantry. All you can do is avoid war at all costs.
A few other general concepts for fast cultural victories:
The Pyramids are very helpful. Representation gives you added benefits for running Artist specialists. And you can speed up the construction of Temples and Cathedrals tremendously by using Universal Suffrage. Among other things this means you will not need to land-grab as much early on, because you can build your last few cities after your culture starts booming outwards and then just rush the necessary buildings in them.
You'll want as many Great Artists as you can get, so a great person pump is important. But as Cabert said, ideally this will not be one of the 3 cities you are targeting for Legendary status, because a city that has to produce both lots of Great Artists and build lots of Cathedrals will be slower at both than separate cities that are more focused.
Getting to Liberalism as quickly as possible is probably more important in a cultural victory than any other type of game. Free Speech is extremely useful. And so is the free tech if you get there first. I almost always take Nationalism, which enables the Hermitage.
I recommend against doing any more research after you get Liberalism. Once you are running Free Speech you should either go all culture immediately, or go all money if you're in a position to cash-rush temples and cathedrals, and then go all culture.
Once you are running all culture, you probably don't need happiness resources anymore. Trade them away for cash (but be careful not to rack up trading with the enemy relationship bonuses). Consider trading them away even earlier if they'll help you get resources that speed up construction of your Cathedrals.